This invention relates to a resistive element formed in a semiconductor substrate.
Preparing a resistive element by diffusing an impurity in a polycrystalline silicon layer is already known. This resistive element comprises a low resistive region in which an impurity is diffused and a high resistive region in which no impurity is diffused. FIGS. 1 and 2 show the conventional resistive element. A low resistive region 12 is constructed by diffusing an impurity with, for example, an SiO.sub.2 layer 10 used as a mask. A high resistive region 14 has no impurity diffused therein. When L is taken to denote the length of the mask, and Xj is taken to represent the length in which an impurity is diffused laterally of the conventional resistive element on one side, then the length of the high resistive region 14 is indicated by L-2Xj.
"Conduction Properties of Lightly Doped Polycrystalline Silicon" written by George J. Korsh and Richard S. Muller in "Solid-State Electronics" vol. 22, pp. 1045-1049 and 1051 discloses that when a voltage V is impressed between both terminals of a polycrystalline silicon layer prepared as described above, the current I flowing through said polycrystalline silicon layer is expressed by the following formula: ##EQU1## EQU I=C(T)sinh qv/2kTN(L-2Xj) where: C(T)=a constant defined by an absolute temperature T and the potential barrier height of an intergrain
k=Boltzmann's constant PA1 N=the number of grains of polycrystalline silicon per unit length of the resistive element PA1 a first semiconductor region formed in a semiconductor substrate with a first impurity concentration; PA1 a second semiconductor region which is formed with a second impurity concentration higher than the first impurity concentration and connected to one end of the first semiconductor region; PA1 a third semiconductor region which is formed with a third impurity concentration higher than the first impurity concentration and connected to the other end of the first semiconductor region; and PA1 said second and third semiconductor regions respectively including a portion having a smaller cross sectional area than the area of a boundary defined by the first semiconductor region and the second and third semiconductor regions.
It is seen from the above formula (1) that in a region where low voltage is impressed, the current varies linearly with said voltage; and in a region where high voltage is impressed, the current increases exponentially relative to said voltage.
The resistive element should preferably be actuated in a linear region of the V-I curve for the stabilization of its properties. Therefore, the greater the length L-2Xj of the high resistive region, the broader the voltage range in which the resistive element can be linearly operated. Since, however, the mask length L cannot be extended much due to restrictions resulting from a demand for the large scale integration of a semiconductor device, an attempt is made to reduce the length Xj in which an impurity is diffused laterally of a resistive element. This attempt is effected by decreasing the temperature at which an impurity is diffused and applying an impurity having a small diffusion coefficient. Where, however, the lateral diffusion length Xj of an impurity is defined as that which is reached when the impurity is diffused at a concentration of 10.sup.17 cm.sup.-3, then the lateral diffusion length Xj possible at present measures about 6 microns, making it necessary to further reduce said length Xj.